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xy is a 2 digit integer whose reverse. . .

This topic has 1 expert reply and 0 member replies

xy is a 2 digit integer whose reverse. . .

Post Fri Sep 22, 2017 10:08 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    xy is a 2 digit integer whose reverse, yx, is x less than twice xy. What is the sum of x and y?

    A) 8
    B) 9
    C) 11
    D) 12
    E) 13

    The OA is E.

    What formula solves this PS question? I couldn't establish it.

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    Post Sun Sep 24, 2017 4:32 am
    Vincen wrote:
    xy is a 2 digit integer whose reverse, yx, is x less than twice xy. What is the sum of x and y?

    A) 8
    B) 9
    C) 11
    D) 12
    E) 13

    The OA is E.

    What formula solves this PS question? I couldn't establish it.
    The 2-digit number [xy] can be represented as 10x + y, thus, its reverse [yx] = 10y + x

    We are given that [yx] = 2*[xy] - x

    10y + x = 2(10x + y) - x

    4y = 9x

    Since 4 and 9 are co-prime, and x and y are single-digit numbers, only possible values of x = 4 and y = 9.

    Thus, the sum of the digits = 4 + 9 = 13.

    The correct answer: E

    Hope this helps!

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    Thanked by: Vincen

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